Suppose that in month #1, in the automotive sector, 100 cars were sold in total. Company A sold 10 of these. In month #2, 90 cars were sold, 9 of these by company A.
When calculating the price elasticity conventionally, the change $dQ/Q$ is negative. But this doesn't take into account the fact that the entire sector went down, and company A actually had a bigger market share and did better. If I ignore that fact, won't my results be misleading? If this indeed needs to be accounted for, how do I modify the usual elasticity formula $d\log Q / d\log P$ ?
Unrelated question: when calculating a time series of point elasticity, the price difference between two observations can be very small, leading to unacceptably large values for the elasticity. How do I deal with this kind of problem?